Misplaced Pages

In geometry, ellipsoid packing is the problem of arranging identical ellipsoid throughout three-dimensional space to fill the maximum possible fraction of space.

The currently densest known packing structure for ellipsoid has two candidates, a simple monoclinic crystal with two ellipsoids of different orientations and a square-triangle crystal containing 24 ellipsoids in the fundamental cell. The former monoclinic structure can reach a maximum packing fraction around ${\displaystyle 0.77073}$ for ellipsoids with maximal aspect ratios larger than ${\displaystyle {\sqrt {3}}}$. The packing fraction of the square-triangle crystal exceeds that of the monoclinic crystal for specific biaxial ellipsoids, like ellipsoids with ratios of the axes ${\displaystyle \alpha :{\sqrt {\alpha }}:1}$ and ${\displaystyle \alpha \in (1.365,1.5625)}$. Any ellipsoids with aspect ratios larger than one can pack denser than spheres.

See also

• Packing problems
• Sphere packing
• Tetrahedron packing

References

1. Donev, Aleksandar; Stillinger, Frank H.; Chaikin, P. M.; Torquato, Salvatore (23 June 2004). "Unusually Dense Crystal Packings of Ellipsoids". Physical Review Letters. 92 (25): 255506. arXiv:cond-mat/0403286. doi:10.1103/PhysRevLett.92.255506.
2. Jin, Weiwei; Jiao, Yang; Liu, Lufeng; Yuan, Ye; Li, Shuixiang (22 March 2017). "Dense crystalline packings of ellipsoids". Physical Review E. 95 (3): 033003. arXiv:1608.07697. doi:10.1103/PhysRevE.95.033003.

• Packing problems